Recently, a number of research have been vigorously made to apply “Chaos Theory” to various industrial fields. Since the chaotic devices evolving chaotically display sensitivity to initial conditions, when two substantially identical devices start with slightly different initial conditions, two identical quickly evolve to values with different trajectories which are vastly different and become totally uncorrelated as time evolves. This makes chaotic devices nonperiodic and unpredictable over long times. The phenomenon is due to the sensitivity to initial conditions which is called Butterfly Effect. In a chaotic system with the master chaotic device and the slave chaotic device, synchronization means that state variables of the master chaotic device become identical to state variables of the slave chaotic device to control the chaotic phenomenon.
However, such chaotic devices are impossible to synchronize by conventional methods. Thus, new numerous methods have been proposed and developed to synchronize signals of nonlinear dynamical devices and also to apply the synchronized chaotic devices to secure communication.
Considering known prior arts, methods are described in papers by Louis M. pecora and Thomas L. Carrol entitled “Synchronization in Chaotic System”(PHYSICAL REVIEW LETTERS, Vol. 4 No.8, p.821, 1990) and entitled “Synchronizing Chaotic Circuits”(IEEE TRANSACTIONS CIRCUIT AND SYSTEMS, p.453, April 1991). These articles disclose a theory of synchronizing two chaotic devices and describe a circuit demonstrating such synchronization. Also, U.S. Pat. No. 5,245,660 to Pecora and Carroll discloses a system for producing synchronized signal.
FIG. 1 shows the synchronization concept disclosed in U.S. Pat. No. 5,245,660 to Pecora and Carroll. Referring to FIG. 1, a primary system as a master chaotic device is divided into first subsystem 2 as a drive signal generator and second subsystem 3. A new subsystem 3′ identical to the subsystem 3 is linked with the primary system 1, there forming a response subsystem 1′ as a slave chaotic device. The master and slave devices construct an overall chaotic system. The driving output signal X4 of the first subsystem 2 is transmitted to the second subsystem 3 and response subsystem 3′ to synchronize the second subsystem 3′ wherein the variables X1′, X2′, X3′ of the response subsystem 3′ correspond to the variables X1, X2, X3 of the second subsystem. As a result, the variables X1′, X2′, X3′, X4′ of the slave chaotic device and the variables X1, X2, X3, X4 of the master chaotic device are in synchronization with each other.
On the other hand, synchronization in chaotic systems has high potentiality of practical applications in secure communication, optics, and nonlinear dynamics model identification. Specially, the secure communication using a synchronizing system is disclosed in U.S. Pat. No. 5,291,555 to Cuomo and Oppenheim which employs the synchronizing concept of Pecora and Carroll thereto.
FIG. 2 shows the communication system disclosed in U.S. Pat. No. 5,291,555 to Cuomo and Oppenheim. The communication system comprises a chaotic transmitter 10 including a drive signal generator 12 for producing a chaotic drive signal u(t) and an adder 14 for adding message signal m(t) to the drive signal u(t) to produce a transmitted signal, and a receiver 20 for receiving the transmitted signal including a drive signal regenerator 22 for reconstructing the drive signal u′(t) from the received signal u(t)+m(t), and a subtracter 24 for subtracting the reconstructed drive signal u′(t) from the received signal u(t)+m(t) to detect therefrom message signal m′(t).
However, there is a drawback that the synchronizing method according to the prior art is applied to single chaotic system having a master chaotic device and a slave chaotic device and may not be applied to a plurality of chaotic systems to successively synchronize the plurality of chaotic systems. Therefore, there is a problem that multichannel communications and stratification of communication participants can not be carried out.